Transcript Slide 1

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Understanding Options Pricing
Steve Meizinger
ISE Education
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Required Reading
For the sake of simplicity, the examples that follow do not take into
consideration commissions and other transaction fees, tax
considerations, or margin requirements, which are factors that may
significantly affect the economic consequences of a given strategy.
An investor should review transaction costs, margin requirements and
tax considerations with a broker and tax advisor before entering into
any options strategy.
Options involve risk and are not suitable for everyone. Prior to buying
or selling an option, a person must receive a copy of
CHARACTERISTICS AND RISKS OF STANDARDIZED OPTIONS.
Copies have been provided for you today and may be obtained from
your broker, one of the exchanges or The Options Clearing
Corporation. A prospectus, which discusses the role of The Options
Clearing Corporation, is also available, without charge, upon request
at 1-888-OPTIONS or www.888options.com. an endorsement,
recommendation or solicitation to buy or sell securities.
Any strategies discussed, including examples using actual securities
price data, are strictly for illustrative and educational purposes and are
not to be construed as an endorsement or recommendation to buy or
sell securities.
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Likelihood of events
» Options pricing is based on the likelihood of an
event occurring
» Terms such as most likely, most unlikely,
probable, improbable, likely, unlikely and
possible describe the likelihood an event
occurring, but not from a specific or quantifiable
perspective
» Options trader’s wanted a more quantifiable
solution, the answer: Black-Scholes Options
Pricing Model
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Where do the prices come from?
» Fisher Black and Myron Scholes developed
the most popular pricing model
» Based on the concept that dynamic
behavior of asset prices is expected
» Assumption of model is risk-neutrality
» Many other models now used, Cox-RossRubenstein is one example, most are
extensions of Black-Scholes
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Pricing models, who cares?
» Laws of probability enable practitioners to predict
the likelihood of events to occur
» Option pricing models are based on the premise
that stock prices are random and cannot be
predicted with any accuracy
» Option values are based on bell-shaped,
lognormal distribution with a slight upward bias
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Efficient or not?
» Efficient Market Hypothesis (EMH) assumes the
market fully reflects all available information
» What about periods of excess volatility, pricing
“bubbles” and the occasional chaos of the
market?
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Option Prices are Based on Probabilities
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Pricing Inputs
» Underlying price
» Strike price
» Time until expiration
» Risk-free rates
» Dividends of underlying
» Volatility
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Underlying Price
» Relationship between the strike price and the
underlying price creates the value of the option at
expiration
» At expiration all options are worth the intrinsic
value or they are worthless
» Option pricing expectations are measured by
delta, the rate option moves based on a one unit
change in the underlying price
» The greater the likelihood of the option expiring
in the money the greater the delta
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Strike Price
» Each option has a strike price at which the
underlying can be bought or sold
» Option strike prices are similar to insurance
policies deductibles
» Various strikes prices offer differing risk/reward
propositions
» Call strikes can be viewed insuring cash
» Put strikes can be viewed insuring underlying
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Time
» In most cases the greater amount of time the
greater the option’s value
» Time decay is not linear, shorter term options
decay faster than longer term (theta)
» Generally the greater the time decay the greater
the potential for a rapidly changing delta (gamma)
» Gamma manufactures delta creating option price
change
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Options have value for 2 reasons
» Cost of carrying underlying position (risk-free
interest rates)
» Potential underlying variance (volatility)
» If rates were 0% and the underlying stock had no
potential for movement all options would trade at
intrinsic value or 0
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Risk-free Rates
» Call options can be viewed as a surrogate for
underlying stock + put option (S + P) = C
» The cost of carrying an underlying position
increases as interest rates increase therefore
calls increase accordingly (rho)
» Puts will fall (by the same amount as calls rise) as
interest rates increase
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Dividends
» Theoretically, stocks should decline by the
dividend amount on the ex-dividend date
» Deep in the money calls will fall by the amount of
the dividend on ex-div date
» All other calls should not be impacted by exdividend
» Deep in the money puts will anticipate this
payment and will typically remain relatively
unchanged on ex-date
» Unexpected changes in dividends will impact
option prices, puts have a positive relationship to
dividends, calls have a negative relationship
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Volatility: The prediction of how much
prices will vary
» How much change is expected?
» Variance as measured by volatility, expected error
factor from the mean
» Risk = Standard deviation
» Price movements within one standard deviation
movements should occur 68% of the time, within
two standard deviations 95%
» Risk/Reward remain in balance, the more growth
the market expects the more risk the stock infers
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The Greeks
» Delta- The change in the option’s value for every one unit
change in the underlying (0.00-1.00)
» Gamma- The change in the option’s delta for every one
change in the underlying (gamma “manufactures delta”)
(i.e. .07). For example, the stock moves up 1 unit and call
delta was .52, new call delta will be .59
» Theta- The change in the option’s value for every one day
decrease in the time remaining until expiration. The dollar
amount of time decay expressed in decimals. If an option
closes at $3.5 with -.20 theta and the stock opens the next
day unchanged, the new theoretical value is $3.3
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The Greeks
» Vega- The change in the option’s value for a one
percentage point increase in implied volatility. Expressed
in decimals. For example if an option had a vega of .25 and
a theoretical value is $2.5, if the volatility were increase by
1% the option would have a new theoretical value of $2.75
» Rho- The change in the option’s value for a one
percentage point increase in risk-free interest rates.
Expressed in decimals, calls and puts have differing values.
For example a Rho of .06 indicates the option’s theoretical
value will increase by .06 given a 1% increase in interest
rates Long calls and short puts have positive rho
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Volatility
» The volatility associated with an asset is stated in
annual percentage, it is a one standard deviation
up or down estimation of future price
» Very concise and powerful way of conveying the
amount of uncertainty in underlying forecasts
» The option’s sensitivity to volatility is measured
by vega, the amount the option will increase by a
1 unit change in volatility
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Types of Volatility
» Historical
» Implied
» Actual-or future
» Your own, your strategy may favor an increase
or decrease in volatility
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Historical Volatility
» Calculate the past history of the mean price of the
underlying stock over a certain period of time (10
day, 30, 60, or 252)
» Calculate the standard deviations for the periods
» Standard deviation is the mathematical term for
risk, or the variance from the average
» The distribution curve graphically describes how
much the stock fluctuated in the past
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Implied Volatility
» Reverse engineering of the Black-Scholes option
pricing model
» Instead of solving for an option’s value, use
market price and solve for implied volatility
» Assumption is market participants are more
knowledgeable than past data
» Many experts believe implied volatility is the best
predictor for future volatility
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Actual Volatility
» What actually occurs in the marketplace
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Forecasting Volatility
» Each option trade includes embedded forecasts,
not only for the underlying, the time period, but
also for volatility
» Differing strike prices are affected differently by
changes in perceived volatility (Vega)
» The longer the time period the greater the impact
of volatility (Vega)
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A Further Look at Implied Volatilities
» Implied volatilities can vary widely, sometimes prior to
announced earnings or government rulings, options can
become more expensive due to the increased risk of the
outcome
» In this case the stock volatility did “lag” the implied volatility
after the announcement, of course this is not always the case
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Volatilities revert back to their
past average price, the mean
» Volatility is always changing
» What time frame do you use to calculate
historical volatilities?
» Question is when will it revert?
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Your Forecast: Volatility is “high”, and
future volatility will be lower than today’s
» Buy call vertical or put vertical spread depending on
your market forecast to mitigate volatility risk
» Covered call, assuming you are bullish
» Long calendar spread
» Sell out of the money call spread and out of the money
put spread (iron condor) with balanced risk
» Sell straddles or strangles albeit with substantially more
downside risk
» Buy butterfly spread, buy in the money spread and sell
at the money spread (buy 95c, sell 100c, sell 100c buy
105c)
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Your Forecast: Volatility is “low”, and
future volatility will be higher than today’s
» Purchase calls or puts
» Buy ratio spread, buy two out of the money
options, sell one at the money
» Buy straddles or strangles hoping to realize
increased stock volatility (breakouts) or
increased implied volatility
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Changing Inputs
INPUT INCREASES
CALL PRICE
PUT PRICE
Strike Price
Down
Up
Stock Price
Up
Down
Time Until Expiration
Up
Up
Risk-free Rates
Up
Down
Down
Up
Up
Up
Dividends
Volatility
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Assumptions for Option Models
» Stock prices are efficient creating a lognormal distribution
» Interest rates are constant (they actually deviate slightly
throughout the term normally)
» Early exercise is not possible (American style options allow
early exercise)
» Volatility is constant (not always true, especially during
stressful market periods)
» Stocks can be borrowed to facilitate hedging (normally true
unless involved in a major corporate development)
» Markets do not gap (Markets do gap creating difficulty for
delta neutral hedging)
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Who cares about all this?
» Without variances in interest rates and volatility,
options would have no value
» Gaining a better understanding of options pricing
allows investors to understand the risk reward
tradeoffs
» Pricing is based on the theory that markets are
random and efficient
» The Black Scholes model, or similar models,
helps give investors guidance on option pricing,
it does not guarantee a certain options price
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Summary
» The Black-Scholes option pricing model, or
similar models, calculates theoretical prices
based on stock price, strike price, time left until
expiration, risk-free interest rates, dividends and
volatility
» Volatility is the most important input that affects
option pricing
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Summary
» A better understanding of the pricing model
inputs can help investors incorporate your own
market expectations with your own risk/return
tradeoffs
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ISEOptions.com
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